• Sets and their representation
• Union, intersection and complement of sets and their algebraic properties
• Power set; Relation, Types of relations, equivalence relations, functions; One-one, into and onto functions, the composition of functions.

• Complex numbers as ordered pairs of reals,
• Representation of complex numbers in the form a+ib and their representation in a plane,
• Argand diagram,
• algebra of complex numbers,
• modulus and argument (or amplitude) of a complex number,
• square root of a complex number,
• triangle inequality,
• Quadratic equations in real and complex number system and their solutions.
• Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots.

• Matrices,
• algebra of matrices,
• types of matrices,
• determinants and
• matrices of order two and three.
• Properties of determinants,
• evaluation of determinants,
• area of triangles using determinants.
• Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations,
• Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

Permutations and combinations

• Fundamental principle of counting,
• permutation as an arrangement and
• combination as selection,
• Meaning of P (n,r) and C (n,r),
• simple applications.

• Principle of Mathematical Induction and its simple applications

• Binomial theorem for a positive integral index,
• general term and middle term,
• properties of Binomial coefficients
• simple applications

• Arithmetic and Geometric progressions,
• insertion of arithmetic,
• geometric means between two given numbers
• relation between A.M. and G.M. sum upto n terms of special series: Sn, Sn², Sn³
• Arithmetic – Geometric progression

• Real – valued functions,
• algebra of functions,
• polynomials,
• rational,
• trigonometric,
• logarithmic and exponential functions,
• inverse functions
• Graphs of simple functions
• Limits, continuity and differentiability
• Differentiation of the sum, difference, product and quotient of two functions
• Differentiation of trigonometric,
• inverse trigonometric,
• logarithmic,
• exponential,
• composite and implicit functions
• derivatives of order upto two
• Rolle’s and Lagrange’s Mean Value Theorems
• Applications of derivatives: Rate of change of quantities, monotonic – increasing and decreasing functions,
• Maxima and minima of functions of one variable,
• tangents and normals

• Integral as an anti – derivative.
• Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions.
• Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities.

• Evaluation of simple integrals of the type Integral as limit of a sum.
• 
• Fundamental Theorem of Calculus.
• Properties of definite integrals.
• Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

• Ordinary differential equations, their order and degree.
• Formation of differential equations.
• Solution of differential equations by the method of separation of variables, solution of homogeneous and linear differential equations of the type: dy/dx+p(x)y=q(x)

• Cartesian system of rectangular co-ordinates 10 in a plane,
• distance formula,
• section formula,
• locus and its equation,
• translation of axes,
• slope of a line,
• parallel and perpendicular lines,
• intercepts of a line on the coordinate axes.

• Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two intersecting lines.
• Skew lines, the shortest distance between them and its equation.
• Equations of a line and a plane in different forms, intersection of a line and a plane, coplanar lines.

• Vectors and scalars,
• addition of vectors,
• components of a vector in two dimensions and three dimensional space,
• scalar and vector products, scalar and vector triple product.

Probability: Probability of an event, addition and multiplication theorems of probability, Baye’s theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution.

• Trigonometrical identities and equations
• Trigonometrical functions
• Inverse trigonometrical functions and their properties
• Heights and Distances

• Statements, logical operations and, or, implies, implied by, if and only if
• Understanding of tautology, contradiction, converse and contrapositive